1. Field of Invention
The present invention relates to communication systems and more specifically to a variable-capacitance circuit.
2. Prior Art
Variable capacitance devices are often used in frequency-selective circuits such as filters, VCOs, etc. These devices may be implemented using any device whose capacitance depends on an applied DC control voltage. Often diodes (so-called “varactors”) are used for this purpose but other devices, for example MOS transistors, may be used, taking advantage of their voltage-dependent CV-curve. In the following, excluding the references, the term “varactor” is to be understood in the broader sense as any kind of variable-capacitance device, not just a diode. Similarly, the varactor symbol shown in FIG. 1 should be construed as any kind of variable-capacitance device. Also, in the following, the “exponent” should be construed as the value of n obtained when the CV-curve is approximated by the following equation:
      C    ⁡          (      V      )        =      K                  (                  ϕ          +          V                )            n      where V is the applied voltage, C=dQ/dV is the incremental diode capacitance, and φ and K are constants. The approximation may be global, covering the entire tuning curve, or local, that is, valid for a region around an operating point voltage V0.
The presence of signal voltage across the varactor instantaneously disturbs the DC voltage and therefore modulates the capacitance. This causes distortion. However, it is possible to use two or more varactors in certain configurations wherein this distortion is minimized.
FIG. 2 shows one such structure, as described in the publication by Meyer and Stephens, entitled “Distortion in Variable-Capacitance Diodes” in the Journal of Solid-State circuits, vol. SC-10, No. 1, February 1975, pp. 47-54, incorporated herein by reference. The publication derives expressions for the non-linear coefficients in the C-V curve (equations 39-42 in the paper and repeated below) and it is shown that, as a special case, complete distortion cancellation can be achieved by choosing the varactor to be of equal size (i.e. DA=DB) and the exponent to be n=0.5.
                              C          ⁡                      (            υ            )                          =                              1                          P              0                                -                                                    2                ⁢                                  P                  1                                                            P                0                3                                      ⁢            υ                    +                                    3                              P                0                5                                      ⁢                          (                                                2                  ⁢                                      P                    1                    2                                                  -                                                      P                    0                                    ⁢                                      P                    2                                                              )                        ⁢                          υ              2                                +                                    (        39        )            where
                              P          0                =                              1                          K              0                                +                      1                          L              0                                                          (        40        )                                          P          1                =                                            K              1                                      2              ⁢                              K                0                3                                              +                                    L              1                                      2              ⁢                              L                0                3                                                                        (        41        )                                          P          2                =                                                                              K                  1                  2                                ⁢                                  /                                ⁢                2                            -                                                K                  0                                ⁢                                  K                  2                                ⁢                                  /                                ⁢                3                                                    K              0              5                                +                                                                                          L                    1                    2                                    ⁢                                      /                                    ⁢                  2                                -                                                      L                    0                                    ⁢                                      L                    2                                    ⁢                                      /                                    ⁢                  3                                                            L                0                5                                      .                                              (        42        )            
In order to achieve sufficiently wide capacitance range, it is often necessary to use varactors with n>0.5 but fortunately the above-mentioned equations show that it is still possible to achieve distortion cancellation. This can be done by choosing DA≠DB. Thus a specific ratio DA/DB can for example give complete cancellation of third-order distortion. The above-mentioned equations are solved for this purpose in the publication by K. Buisman et al., entitled “Distortion-Free Varactor Diode Topologies for RF Adaptivity” in the Microwave Symposium Digest, 2005 IEEE MTT-S International, 12-17 Jun. 2005, pp. 157-160, incorporated herein by reference and the resulting ratio is:
            D      A              D      B        =                    4        ⁢        n            +      1      +                                    12            ⁢                          n              2                                -          3                            2      ⁢              (                  n          +          1                )            where n is the diode exponent.
Unfortunately, this does not necessarily cancel the second-order distortion and, depending on the surrounding circuitry that the diode pair is used in, the generated second-order distortion currents may develop significant second-order distortion voltages across the diode pair, which in turn modulate the capacitance and causes third-order distortion due to a mixing effect. This is explained in the K. Buisman publication.
FIG. 3 shows a solution to this distortion problem. In order to avoid this problem, the K. Buisman paper proposes a topology in which two diode-pairs are used in an anti-parallel configuration, as shown in FIG. 3. Due to the symmetry achieved, second-order distortion is now also eliminated.
In the K. Buisman publication, the technique is applied to varactors in a specialized silicon-on-glass fabrication process. This allows very high quality-factor varactors to be fabricated with very low loss to the substrate. Unfortunately, more standard high-volume planar fabrication technologies usually have significant substrate losses and consequently the application of the anti-parallel technique may cause unacceptable loss of quality factor (Q) in resonant circuits in which it is used.
FIG. 4 shows a simplified form of a tunable filter in a pi configuration.
FIG. 5 shows the application of the anti-parallel pair configuration of the circuit of FIG. 4.
The resistance Rp of FIG. 4 and FIG. 5 models the equivalent parallel resistance of the inductor due to finite Q and resistances rs and capacitances Cs model substrate loss.
It will now be explained why this structure causes increased substrate loss: If, for example, DA>DB then nodes A and C will have higher signal swing than nodes B and D. This causes increased loss in the substrate resistances depicted as ‘rs’ in FIG. 5 and that in turn results in degraded Q.
It is therefore desirable to devise a variable capacitance structures that retains the good distortion properties without the penalty of increased substrate loss.
The above discussion shows that it would be desirable to avoid the anti-parallel configuration but still retain the good distortion properties of the single varactor pair. As mentioned, if the exponent n#0.5 then the two varactors would have to be of different size (DA≠DB) and second-order distortion would occur unless the anti-parallel configuration was used to cancel it. In many applications third order distortion is of overriding concern and the second-order distortion itself is of minor importance. The filter of FIG. 4 is an example of this. Here, a desired signal may be present at the resonance frequency f0 but may be contaminated by third-order distortion products generated by interfering signals at frequencies f1 and f2 close to the resonance frequency where f0=(2f1−f2) or f0=(2f2−f1). Since f1 and f2 are close to f0, the filter may not provide much attenuation of these signals, resulting in high amplitudes across the variable capacitances and hence distortion. By contrast, for a second-order product to be generated at f0 at least one of the interfering signals would have to be far from f0 (the conditions would be f0=(f1+f2), f0=|f1−f2|, f0=2f1, or f0=2f2); it would therefore be attenuated greatly by the filter response. Consequently, at least one of the interfering signals will only be present at very low amplitude across the variable capacitance structures and the generated distortion product will be accordingly small. However, the previously mentioned secondary mixing effect that creates additional third-order products from mixing with the fundamental signals can be of great importance. In order to avoid excessive third-order distortion, it can therefore be necessary to eliminate the second-order products.
As mentioned, the most important third-order distortion condition occurs when two interferers are present at frequencies f1 and f2 that are close to the resonance frequency f0. In addition to the unwanted third-order distortion products 2f1−f2 or 2f2−f1, the second-order distortion of the variable capacitance structures will also generate distortion products at |f1−f2|, (f1+f2), 2f1, and 2f2. These products are not of direct concern because they are far away from the desired signal frequency of f0 but they can modulate the variable capacitances such that a mixing effect can occur, which generates secondary distortion products at several frequencies including the following:|f1+|f1−f2∥=2f1−f2 for f1>f2|f2−|f1−f2∥=2f2−f1 for f1>f2|f2+|f1−f2∥=2f2−f1 for f1<f2|f1−|f1−f2∥=2f1−f2 for f1<f22f2−f12f1−f2
These products fall at the same frequencies as the direct third-order products and are therefore undesirable. Prior art, as described previously, solves this problem by eliminating second-order distortion using either anti-parallel structures or a diode exponent of n=0.5. As mentioned, both solutions have disadvantages.